Quantity A 230 - 229 2 A Quantity A is greater. B Quantity B is greater. Quantity B 228 The two quantities are equal. D The relationship cannot be determined from the information given.
Quantity A 230 - 229 2 A Quantity A is greater. B Quantity B is greater. Quantity B 228 The two quantities are equal. D The relationship cannot be determined from the information given.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Please show step by step process on how to solve this problem. The answer is C but i don't understand why.
![**Comparing Quantities in Exponential Form**
In this exercise, you will compare Quantity A and Quantity B to determine their relationship based on the given mathematical expressions. The possible answers include four options: Quantity A is greater, Quantity B is greater, the two quantities are equal, or the relationship cannot be determined from the information provided.
**Problem:**
- **Quantity A**: \(\frac{2^{30} - 2^{29}}{2}\)
- **Quantity B**: \(2^{28}\)
**Options:**
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
**Analysis:**
Let's break down the expressions to compare the quantities:
For **Quantity A**:
\[ \frac{2^{30} - 2^{29}}{2} \]
1. Factor out \(2^{29}\) from the numerator:
\[ \frac{2^{29}(2 - 1)}{2} \]
2. This simplifies to:
\[ \frac{2^{29} \cdot 1}{2} = \frac{2^{29}}{2} \]
3. Since dividing by 2 is the same as subtracting 1 from the exponent:
\[ 2^{29 - 1} = 2^{28} \]
For **Quantity B**:
\[ 2^{28} \]
After simplifying, both quantities are equal to \(2^{28}\).
**Conclusion:**
The correct answer is:
C. The two quantities are equal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e94b5f2-f208-413f-b143-e0eec596a337%2Ff0d6fc83-92b4-4aaa-a153-a2c0eb6a161e%2F17292mw_processed.png&w=3840&q=75)
Transcribed Image Text:**Comparing Quantities in Exponential Form**
In this exercise, you will compare Quantity A and Quantity B to determine their relationship based on the given mathematical expressions. The possible answers include four options: Quantity A is greater, Quantity B is greater, the two quantities are equal, or the relationship cannot be determined from the information provided.
**Problem:**
- **Quantity A**: \(\frac{2^{30} - 2^{29}}{2}\)
- **Quantity B**: \(2^{28}\)
**Options:**
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
**Analysis:**
Let's break down the expressions to compare the quantities:
For **Quantity A**:
\[ \frac{2^{30} - 2^{29}}{2} \]
1. Factor out \(2^{29}\) from the numerator:
\[ \frac{2^{29}(2 - 1)}{2} \]
2. This simplifies to:
\[ \frac{2^{29} \cdot 1}{2} = \frac{2^{29}}{2} \]
3. Since dividing by 2 is the same as subtracting 1 from the exponent:
\[ 2^{29 - 1} = 2^{28} \]
For **Quantity B**:
\[ 2^{28} \]
After simplifying, both quantities are equal to \(2^{28}\).
**Conclusion:**
The correct answer is:
C. The two quantities are equal.
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